Prove using vectors: The median to the base of an isosceles triangle is perpendicular to the base.

Prove that the angles opposite to equal sides of an isosceles triangle are equal.

Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side. (Using converse of basic proportionality theorem)

Prove that the medians of an equilateral triangle are equal.

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find its length and breadth.

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

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For any triangle, prove that the sum of the sides of the triangle is greater than the sum of the medians of the triangle.

The areas of two similar triangles are 121 cm^(2) and 64 cm^(2) respectively. If the median of the first triangle is 12.1 cm , find the corresponding median of the second triangle.

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.